NS Equations for multiphase flow in porous media

quir · February 13, 2017, 12:00

Hi everyone,

I've been stuck on following problem for a while:

I am trying to model multiphase (gas-liquid) flow through a packed bed for which I am using twoPhaseEulerFoam in OpenFOAM 3.0.1. To my understanding, all I need to do is change following equation
$(1) \alpha_1 + \alpha_2 = 1$
to
$(2) \alpha_1 + \alpha_2 = \epsilon$
where $\epsilon$ is the porosity.
The alpha-equation solved in fluid.solve() is the one suggested by Weller in Rusche's thesis:
$(3) \frac{\partial \alpha_1}{\partial t} + \nabla \cdot (\alpha_1(\alpha_1 \bar{U}_1 + \alpha_2 \bar{U}_2) + (\bar{U}_1 - \bar{U}_2) \alpha_1(1-\alpha_1))=0$
However, this is only valid with equation (1). So, using equation (2) instead, an additional term appears:
$(3) \frac{\partial \alpha_1}{\partial t} + \nabla\cdot (\alpha_1(\alpha_1\bar{U}_1 + \alpha_2\bar{U}_2) + (\bar{U}_1 - \bar{U}_2)\alpha_1(1-\alpha_1) + \alpha_1 \alpha_s U_2)=0$
where $\alpha_s=1-\epsilon$ . I have also added a momentum sink term to the momentum equations to account for liquid-solid and gas-solids interaction. My problem is that the $\alpha$ s are not bounded between 0 and $\epsilon$ , but still go as high as 1.
I have tried defining an alphaMax in phaseProperties which should give a bound for the MULES solver, however, this doesn't make a difference.

Any ideas on what could be the problem?

Thanks

bibin.sme · June 15, 2017, 09:49

Did u get any solution to this problem... can you share your solver... ???

roshanak.rabiee878 · May 25, 2020, 11:48

Hi
have you solved your problem?
I have questions about how you add effect of relative permeability into your solver

Roshanak

Quote:

Originally Posted by quir

Hi everyone,

I've been stuck on following problem for a while:

I am trying to model multiphase (gas-liquid) flow through a packed bed for which I am using twoPhaseEulerFoam in OpenFOAM 3.0.1. To my understanding, all I need to do is change following equation
$(1) \alpha_1 + \alpha_2 = 1$
to
$(2) \alpha_1 + \alpha_2 = \epsilon$
where $\epsilon$ is the porosity.
The alpha-equation solved in fluid.solve() is the one suggested by Weller in Rusche's thesis:
$(3) \frac{\partial \alpha_1}{\partial t} + \nabla \cdot (\alpha_1(\alpha_1 \bar{U}_1 + \alpha_2 \bar{U}_2) + (\bar{U}_1 - \bar{U}_2) \alpha_1(1-\alpha_1))=0$
However, this is only valid with equation (1). So, using equation (2) instead, an additional term appears:
$(3) \frac{\partial \alpha_1}{\partial t} + \nabla\cdot (\alpha_1(\alpha_1\bar{U}_1 + \alpha_2\bar{U}_2) + (\bar{U}_1 - \bar{U}_2)\alpha_1(1-\alpha_1) + \alpha_1 \alpha_s U_2)=0$
where $\alpha_s=1-\epsilon$ . I have also added a momentum sink term to the momentum equations to account for liquid-solid and gas-solids interaction. My problem is that the $\alpha$ s are not bounded between 0 and $\epsilon$ , but still go as high as 1.
I have tried defining an alphaMax in phaseProperties which should give a bound for the MULES solver, however, this doesn't make a difference.

Any ideas on what could be the problem?

Thanks

regard · December 26, 2020, 12:25

hi all

can any body help me please, i want to change my alpha equation for two phase flow in porous media and i need to add effect of relative permeability and capillry pressure
thanks in advance

February 13, 2017, 12:00	NS Equations for multiphase flow in porous media	#1
quir New Member Quirin Grossmann Join Date: Nov 2016 Posts: 1 Rep Power: 0	Hi everyone, I've been stuck on following problem for a while: I am trying to model multiphase (gas-liquid) flow through a packed bed for which I am using twoPhaseEulerFoam in OpenFOAM 3.0.1. To my understanding, all I need to do is change following equation $(1) \alpha_1 + \alpha_2 = 1$ to $(2) \alpha_1 + \alpha_2 = \epsilon$ where $\epsilon$ is the porosity. The alpha-equation solved in fluid.solve() is the one suggested by Weller in Rusche's thesis: $(3) \frac{\partial \alpha_1}{\partial t} + \nabla \cdot (\alpha_1(\alpha_1 \bar{U}_1 + \alpha_2 \bar{U}_2) + (\bar{U}_1 - \bar{U}_2) \alpha_1(1-\alpha_1))=0$ However, this is only valid with equation (1). So, using equation (2) instead, an additional term appears: $(3) \frac{\partial \alpha_1}{\partial t} + \nabla\cdot (\alpha_1(\alpha_1\bar{U}_1 + \alpha_2\bar{U}_2) + (\bar{U}_1 - \bar{U}_2)\alpha_1(1-\alpha_1) + \alpha_1 \alpha_s U_2)=0$ where $\alpha_s=1-\epsilon$ . I have also added a momentum sink term to the momentum equations to account for liquid-solid and gas-solids interaction. My problem is that the $\alpha$ s are not bounded between 0 and $\epsilon$ , but still go as high as 1. I have tried defining an alphaMax in phaseProperties which should give a bound for the MULES solver, however, this doesn't make a difference. Any ideas on what could be the problem? Thanks Last edited by quir; February 14, 2017 at 11:37.

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June 15, 2017, 09:49		#2
bibin.sme New Member Bibin K.S Join Date: Oct 2014 Posts: 19 Rep Power: 12	Did u get any solution to this problem... can you share your solver... ???

December 26, 2020, 12:25		#4
regard Member ... Join Date: May 2018 Posts: 37 Rep Power: 8	hi all can any body help me please, i want to change my alpha equation for two phase flow in porous media and i need to add effect of relative permeability and capillry pressure thanks in advance